IEEE Transactions on Power zyxwvutsrq Systems, Vol. 12, No. 4, November 1997 1569 zy A NEW CONSTRUCTIVE ANN AND ITS APPLICATION TO ELECTRIC LOAD REPRESENTATION zyxw A.P. Alves da Silva C. Ferreira A.C. Zambroni de Soma G. Lambert-Torres Escola Federal de Engenharia de ltajuba (EFEI) BRAZIL Abstract: Accurate dynamic load models allow more precise calculations of power system controls and stability limits. System identification methods can be applied to estimate load models based on measurements. Parametric and nonparametric are the two main classes in system identification methods. The parametric approach has been the only one used for load modeling so far. In this paper, the performance of a nonparametric load model based on a new constructive artificial neural network (Functional Polynomial Network (FPN)) is compared with a linear model and with the popular "ZIP" model. The impact of clustering different load compositions is also investigated. A comparison among the models performance for load chaotic behavior is presented, and some important conclusions are addressed. Substation buses (1 zyxwvutsr 38 kV) from the Brazilian system feeding important industrial consumers have been modeled. Keywords: Load Modeling, Neural Networks, Chaos, Stability Studies. 1. INTRODUCTION The fundamental importance of power system components modeling has already been shown in the literature [I ,21. Regardless of the study to be performed, accurate models for transmission lines, transformers, generators, regulators and compensators have been proposed. However, the same has not occurred for loads. Although the importance of load modeling is well-known, specially for transient and dynamic stability studies, the random nature of a load composition makes its representation very difficult. Two approaches have been used for load modeling. In the first one, based on the knowledge of the individual components, the load model is obtained through the aggregation of the load components models [31. The second approach does not require the knowledge of the load physical characteristics. Based on measurements related to the load responses to disturbances, the model is estimated using system identification methods [4]. The composition approach requires information that is not generally available, which consists in a disadvantage of this method. This approach does not seem to be appropriate since the determination of an average (and precise) composition for each load bus of interest is virtually impossible. The second approach does not suffer from this drawback since the load to be modeled can PE-434-WVRS-0-12-1997 A paper recommended and approved by the IEEE Power System Engineering Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Power Systems. Manuscript submitted July 29, 1996; made available for pririting December 16, 1996. be assumed a "black-box". However, a significant amount of data related to staged tests and natural disturbances affecting the system needs to be collected. Considering the shortcomings of the two approaches, and the fact that data acquisition (and processing) systems are becoming very cheap, it seems that the system identification approach is more in accordance to current technology. This approach allows real-time load monitoring and modeling, which are necessary for on-line stability analysis. Parametric [51 and nonparametric [61 are the two main classes in system identification methods. The parametric methods assume a known model structure with unknown parameters. Methods in this class have been the only ones used for load modeling zyx so far. Their performance depends on a good guess of the model order, which usually requires previous knowledge of the load characteristics. In recent years, artificial neural networks (ANNs) have been used for dynamic load modeling due to features such as nonlinear mapping (universalapproximators) and generalization capability 17- 101. The multilayer perceptron trained with error back propagation has been employed. However, it has several shortcomings such as difficult setting of learning parameters, slow convergence, training failures due to local minima, pre-specified architecture (parametric model). In this paper, the performance of a nonparametric load model based on the Functional Polynomial Network (FPN) [111 is compared with a linear model [41 and with the "ZIP" (constant impedance, current and power) model [31. Chaotic load behavior is analyzed. The impact of clustering different load compositions is also investigated. The paper is organized as follows. Section 2 presents the load models used in this work, where the particular features of each one are shown. Section 3 describes the load clustering technique, whereas Section 4 introduces the autocorrelation function used to identify a chaotic load behavior. Section 5 shows the test results obtained for a real power system and Section 6 presents the conclusions of this work. 2. LOAD MODELS The main idea is to obtain a model that represents the variations of electrical system loads (P and Q), taking into consideration the variations of voltage (V) and frequency (f). The ZIP model, Sections 2.1, is static, while the linear and FPN models, Sections 2.2 and 2.3 respectively, are dynamic. 2.1 ZIP Model The ZIP model is a classic static load model. It is not an accurate model for the majority of power system loads. However, many programs employed by electric utilities use this type of representation. The ZIP model can be expressed by Equation (I), and is also known by constant impedance, constant current and constant power. 0885-8950/97/$10.00 0 1997 IEEE